Paper:

# Positioning Error Calibration of Industrial Robots Based on Random Forest

## Daiki Kato^{*,†}, Kenya Yoshitsugu^{*}, Naoki Maeda^{*}, Toshiki Hirogaki^{*}, Eiichi Aoyama^{*}, and Kenichi Takahashi^{**}

^{*}Doshisha University

1-3 Tataramiyakodani, Kyotanabe, Kyoto 610-0394, Japan

^{†}Corresponding author

^{**}IHI Corporation, Tokyo, Japan

Because most industrial robots are taught using the direct teaching and playback method, they are unsuitable for variable production systems. Alternatively, the offline teaching method has limited applications because of the low accuracy of the position and posture of the end-effector. Therefore, many studies have been conducted to calibrate the position and posture. Positioning errors of robots can be divided into kinematic and non-kinematic errors. In some studies, kinematic errors are calibrated by kinematic models, and non-kinematic errors are calibrated by neural networks. However, the factor of the positioning errors has not been identified because the neural network is a black box. In another machine learning method, a random forest is constructed from decision trees, and its structure can be visualized. Therefore, we used a random forest method to construct a calibration model for the positioning errors and to identify the positioning error factors. The proposed calibration method is based on a simulation of many candidate points centered on the target point. A large industrial robot was used, and the 3D coordinates of the end-effector were obtained using a laser tracker. The model predicted the positioning error from end-effector coordinates, joint angles, and joint torques using the random forest method. As a result, the positioning error was predicted with a high accuracy. The random forest analysis showed that joint 2 was the primary factor of the *X*– and *Z*-axis errors. This suggests that the air cylinder used as an auxiliary to the servo motor of joint 2, which is unique to large industrial robots, is the error factor. With the proposed calibration, the positioning error norm was reduced at all points.

*Int. J. Automation Technol.*, Vol.15, No.5, pp. 581-589, 2021.

- [1] A. Gasparetto and L. Scalera, “From the Unimate to the delta robot: The early decades of industrial robotics,” B. Zhang and M. Ceccarelli (Eds.), “Explorations in the History and Heritage of Machines and Mechanisms,” Springer, pp. 284-295, 2018.
- [2] I. Yasuyuki and T. Kiichi, “Teaching method for industrial robot,” J. of the Robotics Society of Japan, Vol.14, No.6, pp. 780-783, 1996 (in Japanese).
- [3] I. Yoshihisa, V. Drigalski, and F. von Drigalski, “Advances in industrial robots and their effects on manufacturing: A near-future perspective,” J. of the Robotics Society of Japan, Vol.37, No.8, pp. 675-678, 2019 (in Japanese).
- [4] J. Hyun, K. Hyun, and K. Keun, “Calibration of geometric and non-geometric errors of an industrial robot,” Robotica, Vol.19, pp. 311-321, 2001.
- [5] Z. Li, S. Li, and X. Luo, “An Overview of calibration technology of industrial robots,” IEEE/CAA J. of Automatica Sinica, Vol.8, No.1, pp. 23-36, 2021.
- [6] H. Zhuang, Z. Roth, and F. Hamano, “A complete and parametrically continuous kinematic model for robot manipulators,” IEEE Int. Conf. on Robotics and Automation, pp. 92-97, 1990.
- [7] X. Yang, D. Liu, Y. Bai, M. Cong, and Z. Liao, “Kinematics calibration research based on the positioning error of the 6-DOF industrial robot,” Proc. of the 5th Int. Conf. on Cyber Technology in Automation, Control and Intelligent Systems, pp. 1834-1837, 2015.
- [8] J. Lee, G. Park, J. Shin, and J. Woo, “Industrial robot calibration method using Denavit – Hatenberg parameters,” Proc. of the 17th Int. Conf. on Control, Automation and Systems, pp. 913-917, 2017.
- [9] I. Chen and G. Yang, “Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula,” J. of Robotic Systems, Vol.14, No.11, pp. 807-821, 1997.
- [10] R. He, Y. Zhao, S. Yang, and S. Yang, “Kinematic-parameter identification for Serial – Robot calibration based on POE formula,” IEEE Trans. on Robotics, Vol.26, No.3, pp. 411-423, 2010.
- [11] X. Yang, L. Wu, J. Li, and K. Chen, “A minimal kinematic model for serial robot calibration using POE formula,” Robotics and Computer-Integrated Manufacturing, Vol.30, Issue 3, pp. 326-334, 2013.
- [12] A. Nubiola and L. Bonev, “Absolute calibration of an ABB IRB 1600 robot using a laser tracker,” Robotics and Computer-Integrated Manufacturing, Vol.29, Issue 1, pp. 236-245, 2013.
- [13] X. Chen, Q. Zhang, and Y. Sun, “Evolutionary robot calibration and nonlinear compensation methodology based on GA-DNN and an extra compliance error model,” Hindawi Mathematical Problems in Engineering, Vol.2020, 3981081, 2020.
- [14] D. Kato, K. Yoshitsugu, T. Hirogaki, E. Aoyama, and K. Takahashi, “Predicting positioning error and finding features for large industrial robots based on Deep Learning,” Int. J. Automation Technol., Vol.15, No.2, pp. 29-37, 2021.
- [15] S. Aoyagi, M. Suzuki, T. Takahashi, J. Fujioka, and Y. Kamiya, “Calibration of kinematic parameters of robot arm using laser tracking system: Compensation for Non-Geometric Errors by Neural Networks and Selection of Optimal Measuring Points by Genetic Algorithm,” Int. J. Automation Technol., Vol.6, No.1, pp. 29-37, 2012.
- [16] G. Zhao, P. Zhang, G. Ma, and W. Xiao, “System identification of the nonlinear residual errors of an industrial robot using massive measurements,” Robotics and Computer Integrated Manufacturing, Vol.59, pp. 104-114, 2019. ≠wpage
- [17] Y. Wang, Z. Chen, H. Zu, X. Zhang, C. Mao, and Z. Wang, “Improvement of heavy load robot positioning accuracy by combining a model-based identification for geometric parameters and an optimized neural network for the compensation of nongeometric errors,” Hindawi Complexity, Vol.2020, 5896813, 2020.
- [18] B. Yu, “Analysis of a Random Forests model,” J. of Machine Learning Research, Vol.13, pp. 1063-1095, 2012.
- [19] D. Wu, C. Jennings, J. Terpenny, R. Gao, and S. Kumara, “A comparative study on Machine Learning algorithms for smart manufacturing: Tool Wear Prediction Using Random Forests,” J. of Manufacturing Science and Engineering, Vol.139, Issue 7, MANU-16-1567, 2017.
- [20] L. Breiman, “Random forests,” Machine Learning, Vol.45, pp. 5-32, 2001.
- [21] A. Muller and S. Guido, “Introduction to Machine Learning with Python,” O’Reilly Media, Inc., pp. 70-91, 2017.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.